Ed Miliband will criticise Jeremy Clarkson and Janet Street-Porter on Monday for demeaning people with mental health problems, likening attacks on sufferers to the fight against racism, sexism and homophobia.

In his first address since the Labour party conference, where he set out his plan to rebuild Britain as one nation, the Labour leader will propose rewriting the NHS constitution to guarantee that mentally ill people have access to therapies in the same way as the physically ill are provided with drugs and treatment.

With the cost of mental illness to the NHS believed to be around £10bn, Miliband will announce he has set up a taskforce – led by Stephen O'Brien, the chairman of Barts Health NHS Trust and vice-president of Business in the Community – to draw up a strategic plan for mental health in society, in the hope that the next Labour government can begin work immediately on implementing reform.

He will also say that attitudes in society need to change, criticising "lazy caricatures" of people with mental health problems and highlighting recent comments by Clarkson and Street-Porter.

He will say: "There are still people who abuse the privilege of their celebrity to insult, demean and belittle others, such as when Janet Street-Porter says that depression is 'the latest must-have accessory' promoted by the 'misery movement'.

"Jeremy Clarkson at least acknowledges the tragedy of people who end their own life but then goes on to dismisses them as 'Johnny Suicides' whose bodies should be left on train tracks rather than delay journeys.

"Just as we joined the fight against racism, against sexism and against homophobia, so we should join the fight against this form of intolerance. It is not acceptable, it costs Britain dear, and it has to change."

He will liken the failure to tackle mental health as akin to the failure in the past to tackle public health issues such as sanitation and smoking.

Miliband will claim mental health is not just an issue for the health service, saying it means bringing together everyone in Britain to acknowledge, understand and confront this national challenge. The total cost of mental ill health in business is £20bn, he will contend.

The taskforce is likely to look at what can be done to revive the increasing access to the psychological therapies programme that Labour claims is being undermined by cuts enforced on primary care trusts.

The commitment to rewrite the NHS constitution is potentially expensive, but Miliband will argue that the cost of leaving mental illness untreated is higher.

Miliband will warn: "One in four of us will have a mental illness at some point in our lifetime. It is the biggest unaddressed health challenge of our age. There are so many people in Britain today who could be treated but who are intimidated from seeking help. And so many people who need support but who believe that no one will care.

"For far too long our leading politicians have been far too silent about mental health, part of a taboo running across our society which infects both our culture and our politics.

"It is a taboo which not only blights the lives of millions but also puts severe strain on the funding of our NHS and threatens Britain's ability to pay our way in the world. It is a taboo which must be broken if we are to rebuild Britain as one nation.

"In fact, everybody has a part to play. Only a nation acting together can overcome the challenge we face," he will say.